Value your tyres
Accurate modelling of material properties is vital in numerical analyses where changes in material properties can have a significant effect on the results of numerical analyses such as those employed in the modelling of automotive tyres.
Automotive tyre rubber is a hyper elastic amorphous polymer material that, on a microscopic level, consists of long chain molecule networks (randomly-orientated), held together by weak intermolecular bonds. Its force-displacement behaviour is highly non-linear, with a nearly incompressible volumetric response. Vulcanization, the addition of filler material and other processes employed during manufacturing, allows the material’s hardness and strength characteristics to be altered in order to obtain the required material response. As such, the mechanical (stress-strain) response of rubber materials varies significantly from sample to sample.
One of the leading (major) causes of structural degradation and failure within an automobile tyre is over-heating. Under sufficiently high temperatures the rubber regions may undergo thermo-oxidation, which is an irreversible mechanical and chemical decomposition in the presence of oxygen. The release of volatile gasses within the tyre cavity will subsequently result in an increase of the operating pressure and associated temperature values. Several heating cycles may result in a cumulative degradation and subsequent failure of the particular tyre. The ability to predict the rate of heat generation within the rubber regions (under normal operating conditions) accurately, is therefore a crucial factor in safe and reliable tyre design within the industry.
Continuum mechanics based numerical models, such as the Mooney-Rivlin constitutive model, are often used to replicate the non-linear and incompressible behaviour of elastomer (rubber) materials within Finite Element (FE) based environments. These are invariant based treatments that model the strain-energy response of the material due to deformation. During the cyclic loading (rotation) of an automobile tyre a fraction of the total input (elastic) deformation energy is absorbed and converted to heat (loss) energy. This phenomenon, called hysteresis heating, occurs due to an inherent phase lag that exists between the stress-strain response curves of such a material. The ratio of loss energy to total energy is defined as the materials hysteresis coefficient. If the material model coefficients and specific hysteresis coefficient values are known, it is possible to predict the rate of heat generated due to hysteresis accurately.
The coefficient values for such numerical rubber models are readily obtainable from direct curve fits of the model equation onto experimentally obtained stress-strain data curves. Provided that the fitting procedure has been executed appropriately, the resulting coefficients will then provide a means to replicate the particular observed material response. The model’s prediction accuracy will however only (at best) be as good as the fit of the theoretical data to the original experimental data, within the particular strain range of interest. Within a FE simulation environment the particular coefficient values will replicate the response (structural and thermal) of the experimentally tested material only.
This Technical Tip highlights the complexities of modelling components we take for granted on a daily basis and the necessity of using appropriate experimental data in numerical modelling. It also highlights that material property data in such rubber materials exhibits a wider spread in mechanical performance (even when the material is manufactured to the same specification) than more traditional engineering of materials such as steels. An important point to acknowledge!
Published in Technical Tips by Origen Engineering Solutions on 1 March 2017